Recent content by gerben

You can download a scanned PDF version (or versions in other formats) here: http://archive.org/details/worksofarchimede00arch In the PDF version the chapter "On the Sphere and Cylinder I" starts at page 193.

The way you drew it case A and case B are the same, (about) the same angle alpha and beta (alpha around 200 degrees and beta around 45 degrees) and since they are somewhat opposite you get a positive number. In case C you will also get a positive number, it is about -cos(100 - 250)

\cos(\alpha - \beta) is 1 when they are in the same direction and -1 when they are in opposite direction. When they are somewhat in the same direction it is smaller than 1 but still positive (the smaller the less they are in the same direction) and when they are somewhat in the opposite...

Moreover, the distance from (each of) your eye(s) to the tip of your finger is not the same for every orientation of your stretched arm.

if x is not equal to y then either x<y or y<x which both imply that x^n is not equal to y^n

is it not much easier to say that since b > a we must have b = a + c for some c larger than 0, so b^2= a^2 + ...

Coulomb's law is about how much force an individual point charge exerts on some other point charge at a distance, i.e. the force goes down quickly with distance. The force that is important in the wire is the force between the electrons in the wire. The force between the electrons next to each...

Correct!

No, when solving f(g(5)), meaning f of g of 5, you go like this: First: What is g(5)? You saw g of 5 is 3, because when x=5 then g(x)=3. Next: what is f(g(5))... hmm, I know g(5)=3, so the question is: "what is f(3)?"

Indeed, so f(5)=-3 and g(5)=3. You were asked "what is f(g(5))". Now that you know what g(5) is, call it b, you can find out what f(g(5)) is. It is equal to f(b).

No, rows are horizontal, columns are vertical. The x row is the top row, move horizontally to where x=5, below that you see what f(x) is when x=5 and again one below you see what g(x) is when x=5

No, to see what g(5) is, you should just check in which column x equals 5 and see what g(x) is in that column.

No, what is g(5)?

Oh sorry, you need to find the f of g of 5 (not the g of f of 5), my original post should have been: Check in which column x=5 and see what g(x) is in that column, you then know what g of 5 is, now find out what the f of g of 5 is by following the same procedure as you did for finding the g of x.

Check in which column x=5 and see what f(x) is in that column, you then know what f of 5 is, now find out what the g of f of 5 is by following the same procedure as you did for finding the f of x.